Writing and Evaluating Expressions with Exponents

You would write it as $7^{3}$, indicating that $7$ is used as a factor three times.

You would write it as $9^{4}$, indicating that $9$ is used as a factor four times.

The expression is $6^{5}$.

You would write it as $5^{3}$, indicating that $5$ is multiplied by itself three times.

The expression is $11^{4}$, showing that $11$ is used as a factor four times.

You would write it as $2^{6}$, indicating six uses of $2$ as a factor.

The expression is $5^{5}$.

The expression is $8^{3}$.

The expression is $2^{4}$.

You would write it as $3^{6}$.

The simplified form is $4^{7}$.

The expression is $10^{5}$.

An exponent indicates how many times a base number is to be used as a factor in multiplication.

A negative exponent, such as $-n$, means you take the reciprocal of the base and then apply the exponent as a positive, writing it as 1/baseⁿ.

For the expression $3^{2}$ x 2, first calculate $3^{2}$, which is 9, and then multiply by 2 to get 18 as the final result.

Understanding exponents is important because they are used to simplify expressions, solve equations, and handle very large or small numbers efficiently.

The basic rules are multiplying powers with the same base (add exponents), dividing powers with the same base (subtract exponents), raising a power to a power (multiply exponents), and understanding zero and negative exponents.

To avoid mistakes, double-check your work, practice regularly, memorise the rules, and ask for help if needed.

Exponents are used in exponential growth and decay scenarios, compound interest calculations, and scientific notation to express large or small numbers.

The order of operations ensures that calculations are performed systematically and accurately, particularly when expressions include multiple operations.

Simplify by multiplying the exponents together. For example, (x²)³ becomes x⁶.

A zero exponent means that any base (except 0) raised to the power of zero equals 1, as in $5^{0}$, which equals 1.