Pair each basic algebraic expression with its correctly simplified result by applying the … — Armed Services Vocational Aptitude Battery (ASVAB)

Pair each basic algebraic expression with its correctly simplified result by applying the fundamental laws of exponents.

The correct pairings are:

m^6 \cdot m^2

with

m^8

;

\frac{n^8}{n^5}

with

n^3

;

(p^4)^3

with

p^{12}

; and

q^{-5}

with

\frac{1}{q^5}

Each expression can be simplified by directly applying one specific fundamental property of exponents.

m^6 \cdot m^2

uses the product rule.

\frac{n^8}{n^5}

uses the quotient rule.

(p^4)^3

uses the power rule.

q^{-5}

uses the negative exponent definition.

Simplify the product expression

m^6 \cdot m^2

m^8

When bases are identical and multiplied, their exponents are added together.

Simplify the quotient expression

\frac{n^8}{n^5}

n^3

When dividing identical bases, the exponent of the denominator is subtracted from the exponent of the numerator.

Simplify the nested power expression

(p^4)^3

p^{12}

When raising an exponent to another power, the two exponents are multiplied.

Rewrite the negative exponent expression

q^{-5}

\frac{1}{q^5}

A negative exponent indicates taking the reciprocal of the base raised to the positive exponent.

Applying fundamental exponent rules (product, quotient, power, and negative exponents) to simplify single-variable expressions.

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