The positive exponential function of {a^{-3}· a^{-4}}{a^{-5}} is:

Correct Answer is : 1a21/a²a21

Correct Answer is : 1a21/a²a21

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Surds and Indices Practice Test 1

Question : 7 of 40

Marks: +1, -0

\frac{a^{-3}\cdot a^{-4}}{a^{-5}}

is:

Solution:

Concept:

Use index laws to combine powers with the same base.

A negative exponent is rewritten as a reciprocal to make it positive.

Explanation:

The expression is

\frac{a^{-3}\cdot a^{-4}}{a^{-5}}

In the numerator, apply the product law:

a^{-3}\cdot a^{-4}=a^{-3+(-4)}=a^{-7}

Now apply the quotient law:

\frac{a^{-7}}{a^{-5}}=a^{-7-(-5)}=a^{-2}

To write it with a positive exponent, use

a^{-m}=\frac{1}{a^m}

So,

a^{-2}=\frac{1}{a^2}

Thus the positive exponential form is

\frac{1}{a^2}

Answer:

\frac{1}{a^2}

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