Equations Involving Indices (Leaving Cert Mathematics): Quizzes

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Equations Involving Indices
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What is the fundamental rule for solving index equations when ax=aya^x = a^y?

x=yx = y

What is an equation involving indices?

An equation where the unknown variable appears as an exponent

What is the first step in solving index equations?

Express both sides with the same base

Solve 7x=717^x = 7^1.

x=1x = 1

What does a−na^{-n} equal?

1an\frac{1}{a^n}

Solve 3x=1273^x = \frac{1}{27}.

x=−3x = -3

How is a\sqrt{a} expressed as a power?

a12a^{\frac{1}{2}}

Simplify (am)n(a^m)^n using the power of a power rule.

amna^{mn}

Solve 4x=164^x = 16 by expressing as powers of 2.

x=2x = 2

What is the reciprocal form of 1an\frac{1}{a^n}?

a−na^{-n}

Solve 25x=112525^x = \frac{1}{125} using base 5.

x=−112x = -1\frac{1}{2}

Express 813\frac{81}{\sqrt{3}} as a power of 3.

3723^{\frac{7}{2}}

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