Last updated on Oct 23, 2026

Solving Equations with Indices (Junior Cert Mathematics): Quizzes

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Solving Equations with Indices

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In the expression $2^3$ , what is the number $3$ called?

The index

In the expression $2^3$ , what is the number $2$ called?

The base

What does $a^0$ equal according to the laws of indices?

$1$

What does $a^{-p}$ equal according to the laws of indices?

$\frac{1}{a^p}$

If $a^x = a^y$ , what can we conclude about $x$ and $y$ ?

$x = y$

Solve $2^x = 16$ .

$x = 4$

Solve $3^{2x-1} = 27$ .

$x = 2$

Solve $5^x = \frac{1}{5}$ .

$x = -1$

Solve $2^{x+1} = 8$ .

$x = 2$

Solve $4^{2x} = 4$ .

$x = \frac{1}{2}$

What is the first step when solving equations with indices?

Express both sides with same base

Using the law $a^p \times a^q = a^{p+q}$ , simplify $2^3 \times 2^5$ .

$2^8$

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