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

Combination of different basesComplete the equationPresenting powers in the denominator as powers with negative exponentsUsing multiple rulesApplying the formulaVariable in the exponent 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:

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

Question 2

Insert the corresponding expression:

\( \left(\frac{4}{a\times b}\right)^2= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{5}{x\times y}\right)^5= \)

Question 4

Insert the corresponding expression:

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

Question 5

Insert the corresponding expression:

\( \left(\frac{6}{x\times y}\right)^2= \)

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

Exercise #1

Insert the corresponding expression:

(2×a3)2= \left(\frac{2\times a}{3}\right)^2=

Video Solution

Answer

All answers are correct

Exercise #2

Insert the corresponding expression:

(4a×b)2= \left(\frac{4}{a\times b}\right)^2=

Video Solution

Answer

42(a×b)2 \frac{4^2}{\left(a\times b\right)^2}

Exercise #3

Insert the corresponding expression:

(5x×y)5= \left(\frac{5}{x\times y}\right)^5=

Video Solution

Answer

a'+b' are correct

Exercise #4

Insert the corresponding expression:

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

Video Solution

Answer

63x3 \frac{6^3}{x^3}

Exercise #5

Insert the corresponding expression:

(6x×y)2= \left(\frac{6}{x\times y}\right)^2=

Video Solution

Answer

36(x×y)2 \frac{36}{\left(x\times y\right)^2}

Question 1

Insert the corresponding expression:

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

Question 2

Insert the corresponding expression:

\( \left(\frac{a}{b}\right)^9= \)

Question 3

Insert the corresponding expression:

\( \left(\frac{a\times3}{2\times x}\right)^3= \)

Question 4

Insert the corresponding expression:

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

Question 5

Insert the corresponding expression:

\( \left(\frac{a\times b}{x\times y}\right)^2= \)

Exercise #6

Insert the corresponding expression:

(a3)2= \left(\frac{a}{3}\right)^2=

Video Solution

Answer

a232 \frac{a^2}{3^2}

Exercise #7

Insert the corresponding expression:

(ab)9= \left(\frac{a}{b}\right)^9=

Video Solution

Answer

a9b9 \frac{a^9}{b^9}

Exercise #8

Insert the corresponding expression:

(a×32×x)3= \left(\frac{a\times3}{2\times x}\right)^3=

Video Solution

Answer

a3×278×x3 \frac{a^3\times27}{8\times x^3}

Exercise #9

Insert the corresponding expression:

(a×b2×x)3= \left(\frac{a\times b}{2\times x}\right)^3=

Video Solution

Answer

a3×b38×x3 \frac{a^3\times b^3}{8\times x^3}

Exercise #10

Insert the corresponding expression:

(a×bx×y)2= \left(\frac{a\times b}{x\times y}\right)^2=

Video Solution

Answer

A'+C' are correct

Question 1

Insert the corresponding expression:

\( \left(\frac{a\times x}{7}\right)^6= \)

Question 2

Insert the corresponding expression:

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

Question 3

Insert the corresponding expression:

\( \left(\frac{x\times a}{b\times y}\right)^4= \)

Question 4

Insert the corresponding expression:

\( \left(\frac{x}{y}\right)^8= \)

Question 5

\( \)

Insert the corresponding expression:

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

Exercise #11

Insert the corresponding expression:

(a×x7)6= \left(\frac{a\times x}{7}\right)^6=

Video Solution

Answer

a6×x676 \frac{a^6\times x^6}{7^6}

Exercise #12

Insert the corresponding expression:

(b5)4= \left(\frac{b}{5}\right)^4=

Video Solution

Answer

b454 \frac{b^4}{5^4}

Exercise #13

Insert the corresponding expression:

(x×ab×y)4= \left(\frac{x\times a}{b\times y}\right)^4=

Video Solution

Answer

x4×a4(b×y)4 \frac{x^4\times a^4}{\left(b\times y\right)^4}

Exercise #14

Insert the corresponding expression:

(xy)8= \left(\frac{x}{y}\right)^8=

Video Solution

Answer

x8y8 \frac{x^8}{y^8}

Exercise #15

Insert the corresponding expression:

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

Video Solution

Answer

57y7 \frac{5^7}{y^7}

Question 1

Insert the corresponding expression:

\( \frac{3^5}{x^5}= \)

Question 2

Insert the corresponding expression:

\( \frac{36\times x^2}{7^2\times b^2}= \)

Question 3

Insert the corresponding expression:

\( \frac{3^8\times a^8}{x^8\times5^8}= \)

Question 4

Insert the corresponding expression:

\( \frac{4^6}{a^6\times x^6}= \)

Question 5

Insert the corresponding expression:

\( \frac{4^9\times b^9}{x^9\times y^9}= \)

Exercise #16

Insert the corresponding expression:

35x5= \frac{3^5}{x^5}=

Video Solution

Answer

(3x)5 \left(\frac{3}{x}\right)^5

Exercise #17

Insert the corresponding expression:

36×x272×b2= \frac{36\times x^2}{7^2\times b^2}=

Video Solution

Answer

(6×x7×b)2 \left(\frac{6\times x}{7\times b}\right)^2

Exercise #18

Insert the corresponding expression:

38×a8x8×58= \frac{3^8\times a^8}{x^8\times5^8}=

Video Solution

Answer

(3×ax×5)8 \left(\frac{3\times a}{x\times5}\right)^8

Exercise #19

Insert the corresponding expression:

46a6×x6= \frac{4^6}{a^6\times x^6}=

Video Solution

Answer

(4a×x)6 \left(\frac{4}{a\times x}\right)^6

Exercise #20

Insert the corresponding expression:

49×b9x9×y9= \frac{4^9\times b^9}{x^9\times y^9}=

Video Solution

Answer

a'+b' are correct