Question

Which expression is equivalent to (r Superscript negative 7 Baseline) Superscript 6? r Superscript 42 StartFraction 1 Over r Superscript 42 Baseline EndFraction Negative 7 r Superscript 6 StartFraction 1 Over r EndFraction.

Answer 1

Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers. The expression which is equal to the given expression is,

$\dfrac{1}{(r)^{42}}$

The option B is the correct option.

Given information-

The given expression in the problem is,

$[(r)^{-7}]^5$

Power rule of exponents

Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers.

Suppose x is a number with power a. The power is power of the power of number x. Then by the power rule of the exponents,

$(x^a)^b=x^{ab}$

Using the power rule of the exponents given expression can be written as,

$[(r)^{-7}]^6=(r)^{-7\times 6}$

$[(r)^{-7}]^6=(r)^{-42}$

Negative exponents rule

Negative exponents rule says that when a power of a number is negative, then write the number in the denominator with the same power with positive sign.Thus,

$[(r)^{-7}]^6=\dfrac{1}{(r)^{42}}$

Hence the expression which is equal to the given expression is,

$\dfrac{1}{(r)^{42}}$

The option B is the correct option.

Learn more about the power rule of exponents here;

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