Powers of a Fraction: Variable in the exponent of the power

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

Insert the corresponding expression:

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

Question 2

Insert the corresponding expression:

\( \left(\frac{2\times7\times21}{5\times6}\right)^x= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{3}{2\times5}\right)^x= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{3\times4}{5\times11\times9}\right)^y= \)

Question 5

Insert the corresponding expression:

\( \left(\frac{11}{19}\right)^{a+3b}= \)

Examples with solutions for Powers of a Fraction: Variable in the exponent of the power

Exercise #1

Insert the corresponding expression:

(23)a= \left(\frac{2}{3}\right)^a=

Video Solution

Answer

2a3a \frac{2^a}{3^a}

Exercise #2

Insert the corresponding expression:

(2×7×215×6)x= \left(\frac{2\times7\times21}{5\times6}\right)^x=

Video Solution

Answer

2x×7x×21x5x×6x \frac{2^x\times7^x\times21^x}{5^x\times6^x}

Exercise #3

Insert the corresponding expression:

(32×5)x= \left(\frac{3}{2\times5}\right)^x=

Video Solution

Answer

3x2x×5x \frac{3^x}{2^x\times5^x}

Exercise #4

Insert the corresponding expression:

(3×45×11×9)y= \left(\frac{3\times4}{5\times11\times9}\right)^y=

Video Solution

Answer

a'+b' are correct

Exercise #5

Insert the corresponding expression:

(1119)a+3b= \left(\frac{11}{19}\right)^{a+3b}=

Video Solution

Answer

11a+3b19a+3b \frac{11^{a+3b}}{19^{a+3b}}

Question 1

Insert the corresponding expression:

\( \left(\frac{2}{3\times5\times7}\right)^x= \)

Question 2

Insert the corresponding expression:

\( \left(\frac{2}{3\times7\times5}\right)^{a+2}= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{2\times4\times5}{7}\right)^a= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{2\times8}{7\times19}\right)^{2x+3y}= \)

Question 5

Insert the corresponding expression:

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

Exercise #6

Insert the corresponding expression:

(23×5×7)x= \left(\frac{2}{3\times5\times7}\right)^x=

Video Solution

Answer

2x3x×5x×7x \frac{2^x}{3^x\times5^x\times7^x}

Exercise #7

Insert the corresponding expression:

(23×7×5)a+2= \left(\frac{2}{3\times7\times5}\right)^{a+2}=

Video Solution

Answer

2a+2(3×7×5)a+2 \frac{2^{a+2}}{\left(3\times7\times5\right)^{a+2}}

Exercise #8

Insert the corresponding expression:

(2×4×57)a= \left(\frac{2\times4\times5}{7}\right)^a=

Video Solution

Answer

2a×4a×5a7a \frac{2^a\times4^a\times5^a}{7^a}

Exercise #9

Insert the corresponding expression:

(2×87×19)2x+3y= \left(\frac{2\times8}{7\times19}\right)^{2x+3y}=

Video Solution

Answer

22x+3y×82x+3y72x+3y×192x+3y \frac{2^{2x+3y}\times8^{2x+3y}}{7^{2x+3y}\times19^{2x+3y}}

Exercise #10

Insert the corresponding expression:

(34)x= \left(\frac{3}{4}\right)^x=

Video Solution

Answer

3x4x \frac{3^x}{4^x}

Question 1

Insert the corresponding expression:

\( \left(\frac{3\times7}{4\times8}\right)^{b+1}= \)

Question 2

Insert the corresponding expression:

\( \left(\frac{5}{9}\right)^{2x+1}= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{5\times11}{3\times7}\right)^a= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{5\times6\times7}{9}\right)^{2x+1}= \)

Question 5

Insert the corresponding expression:

\( \left(\frac{5\times6\times7}{9\times11\times13}\right)^b= \)

Exercise #11

Insert the corresponding expression:

(3×74×8)b+1= \left(\frac{3\times7}{4\times8}\right)^{b+1}=

Video Solution

Answer

3b+1×7b+14b+1×8b+1 \frac{3^{b+1}\times7^{b+1}}{4^{b+1}\times8^{b+1}}

Exercise #12

Insert the corresponding expression:

(59)2x+1= \left(\frac{5}{9}\right)^{2x+1}=

Video Solution

Answer

52x+192x+1 \frac{5^{2x+1}}{9^{2x+1}}

Exercise #13

Insert the corresponding expression:

(5×113×7)a= \left(\frac{5\times11}{3\times7}\right)^a=

Video Solution

Answer

A'+C' are correct

Exercise #14

Insert the corresponding expression:

(5×6×79)2x+1= \left(\frac{5\times6\times7}{9}\right)^{2x+1}=

Video Solution

Answer

a'+b' are correct

Exercise #15

Insert the corresponding expression:

(5×6×79×11×13)b= \left(\frac{5\times6\times7}{9\times11\times13}\right)^b=

Video Solution

Answer

5b×6b×7b9b×11b×13b \frac{5^b\times6^b\times7^b}{9^b\times11^b\times13^b}

Question 1

Insert the corresponding expression:

\( \left(\frac{6}{11\times13\times15}\right)^{xy}= \)

Question 2

\( \)

Insert the corresponding expression:

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

Question 3

Insert the corresponding expression:

\( \frac{1}{\left(2\times b\right)^{-y}}= \)

Exercise #16

Insert the corresponding expression:

(611×13×15)xy= \left(\frac{6}{11\times13\times15}\right)^{xy}=

Video Solution

Answer

A+B are correct

Exercise #17

Insert the corresponding expression:

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

Video Solution

Answer

5ax7ax \frac{5^{ax}}{7^{ax}}

Exercise #18

Insert the corresponding expression:

1(2×b)−y= \frac{1}{\left(2\times b\right)^{-y}}=

Video Solution

Answer

a'+b' are correct