Powers of a Fraction: Calculating powers with negative exponents

Combination of different basesComplete the equationPresenting powers in the denominator as powers with negative exponentsUsing multiple rulesApplying the formulaVariable in the exponent of the powerVariable in the base of the powerInverse formulaNumber of termsconverting Negative Exponents to Positive ExponentsSystem of equations with no solution
Question 1

\( (\frac{2}{3})^{-4}=\text{?} \)

Question 2

\( 7^4\cdot8^3\cdot(\frac{1}{7})^4=\text{?} \)

Question 3

\( (\frac{13}{2})^0\cdot(\frac{2}{13})^{-2}\cdot(\frac{13}{2})^{-5}=\text{?} \)

Question 4

Insert the corresponding expression:

\( \left(\frac{4}{9}\right)^{-5}= \)

Question 5

Insert the corresponding expression:

\( \left(\frac{10}{13}\right)^{-4}= \)

Examples with solutions for Powers of a Fraction: Calculating powers with negative exponents

Exercise #1

(23)−4=? (\frac{2}{3})^{-4}=\text{?}

Video Solution

Step-by-Step Solution

We use the formula:

(ab)−n=(ba)n (\frac{a}{b})^{-n}=(\frac{b}{a})^n

Therefore, we obtain:

(32)4 (\frac{3}{2})^4

We use the formula:

(ba)n=bnan (\frac{b}{a})^n=\frac{b^n}{a^n}

Therefore, we obtain:

3424=3×3×3×32×2×2×2=8116 \frac{3^4}{2^4}=\frac{3\times3\times3\times3}{2\times2\times2\times2}=\frac{81}{16}

Answer

8116 \frac{81}{16}

Exercise #2

74⋅83⋅(17)4=? 7^4\cdot8^3\cdot(\frac{1}{7})^4=\text{?}

Video Solution

Step-by-Step Solution

We use the formula:

(ab)n=anbn (\frac{a}{b})^n=\frac{a^n}{b^n}

We decompose the fraction inside of the parentheses:

(17)4=1474 (\frac{1}{7})^4=\frac{1^4}{7^4}

We obtain:

74×83×1474 7^4\times8^3\times\frac{1^4}{7^4}

We simplify the powers: 74 7^4

We obtain:

83×14 8^3\times1^4

Remember that the number 1 in any power is equal to 1, thus we obtain:

83×1=83 8^3\times1=8^3

Answer

83 8^3

Exercise #3

(132)0⋅(213)−2⋅(132)−5=? (\frac{13}{2})^0\cdot(\frac{2}{13})^{-2}\cdot(\frac{13}{2})^{-5}=\text{?}

Video Solution

Answer

(213)3 (\frac{2}{13})^3

Exercise #4

Insert the corresponding expression:

(49)−5= \left(\frac{4}{9}\right)^{-5}=

Video Solution

Answer

4−59−5 \frac{4^{-5}}{9^{-5}}

Exercise #5

Insert the corresponding expression:

(1013)−4= \left(\frac{10}{13}\right)^{-4}=

Video Solution

Answer

10−413−4 \frac{10^{-4}}{13^{-4}}

Question 1

Insert the corresponding expression:

\( \left(\frac{2}{3}\right)^{-11}= \)

Question 2

Insert the corresponding expression:

\( \left(\frac{1}{4}\right)^{-2}= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{2}{5}\right)^{-3}= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{3}{7}\right)^{-4}= \)

Question 5

Insert the corresponding expression:

\( \left(\frac{1}{20}\right)^{-7}= \)

Exercise #6

Insert the corresponding expression:

(23)−11= \left(\frac{2}{3}\right)^{-11}=

Video Solution

Answer

2−113−11 \frac{2^{-11}}{3^{-11}}

Exercise #7

Insert the corresponding expression:

(14)−2= \left(\frac{1}{4}\right)^{-2}=

Video Solution

Answer

1−24−2 \frac{1^{-2}}{4^{-2}}

Exercise #8

Insert the corresponding expression:

(25)−3= \left(\frac{2}{5}\right)^{-3}=

Video Solution

Answer

2−35−3 \frac{2^{-3}}{5^{-3}}

Exercise #9

Insert the corresponding expression:

(37)−4= \left(\frac{3}{7}\right)^{-4}=

Video Solution

Answer

3−47−4 \frac{3^{-4}}{7^{-4}}

Exercise #10

Insert the corresponding expression:

(120)−7= \left(\frac{1}{20}\right)^{-7}=

Video Solution

Answer

207 20^7

Question 1

Insert the corresponding expression:

\( \left(\frac{5}{7}\right)^{-7}= \)

Question 2

Insert the corresponding expression:

\( \left(\frac{10}{13}\right)^{-2}= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{15}{21}\right)^{-3}= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{1}{60}\right)^{-4}= \)

Question 5

Insert the corresponding expression:

\( \left(\frac{2}{5}\right)^{-2}= \)

Exercise #11

Insert the corresponding expression:

(57)−7= \left(\frac{5}{7}\right)^{-7}=

Video Solution

Answer

(75)7 \left(\frac{7}{5}\right)^7

Exercise #12

Insert the corresponding expression:

(1013)−2= \left(\frac{10}{13}\right)^{-2}=

Video Solution

Answer

(1310)2 \left(\frac{13}{10}\right)^2

Exercise #13

Insert the corresponding expression:

(1521)−3= \left(\frac{15}{21}\right)^{-3}=

Video Solution

Answer

(2115)3 \left(\frac{21}{15}\right)^3

Exercise #14

Insert the corresponding expression:

(160)−4= \left(\frac{1}{60}\right)^{-4}=

Video Solution

Answer

604 60^4

Exercise #15

Insert the corresponding expression:

(25)−2= \left(\frac{2}{5}\right)^{-2}=

Video Solution

Answer

(52)2 \left(\frac{5}{2}\right)^2

Question 1

Insert the corresponding expression:

\( \)\( \left(\frac{1}{3}\right)^{-4}= \)

Question 2

Insert the corresponding expression:

\( \left(\frac{3}{8}\right)^{-5}= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{5}{6}\right)^{-3}= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{10}{17}\right)^{-5}= \)

Question 5

Insert the corresponding expression:

\( \left(\frac{8}{17\times13}\right)^{-6}= \)

Exercise #16

Insert the corresponding expression:

(13)−4= \left(\frac{1}{3}\right)^{-4}=

Video Solution

Answer

34 3^4

Exercise #17

Insert the corresponding expression:

(38)−5= \left(\frac{3}{8}\right)^{-5}=

Video Solution

Answer

(83)5 \left(\frac{8}{3}\right)^5

Exercise #18

Insert the corresponding expression:

(56)−3= \left(\frac{5}{6}\right)^{-3}=

Video Solution

Answer

(65)3 \left(\frac{6}{5}\right)^3

Exercise #19

Insert the corresponding expression:

(1017)−5= \left(\frac{10}{17}\right)^{-5}=

Video Solution

Answer

(1710)5 \left(\frac{17}{10}\right)^5

Exercise #20

Insert the corresponding expression:

(817×13)−6= \left(\frac{8}{17\times13}\right)^{-6}=

Video Solution

Answer

A+B are correct