Question

In which expression should the exponents be multiplied?

Answer 1

Answer:

  D.  (2^6)^-5

Step-by-step explanation:

The exponent rules are ...

$a^ba^c=a^{b+c}\\\\(a^b)^c=a^{bc}$

Exponents are multiplied when an exponential expression is raised to a power.

A.

$\left(\dfrac{1}{5}\right)^2\left(\dfrac{1}{5}\right)^6=\left(\dfrac{1}{5}\right)^{2+6}=\left(\dfrac{1}{5}\right)^8 \quad\text{exponents added}$

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B.

$\dfrac{9^3}{9^4}=(9^3)(9^{-4})=9^{3-4}=9^{-1} \quad\text{exponents added}$

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C.

$(7^3)(7^{8})=7^{3+8}=7^{11} \quad\text{exponents added}$

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D.

$(2^6)^{-5}=2^{6(-5)}=2^{-30} \quad\text{\bf{exponents multiplied}}$

Answer 2

Answer:

the answer is D

Step-by-step explanation: