Indices (Exponents) - Free MCQ Practice Test with solutions, Class 9 Mathematics

The expression \( a^{m/n} \) is equivalent to the nth root of \( a \) raised to the power of \( m \), or \( \sqrt[n]{a^m} \).

This simplifies to \( \frac{x^{2 \times 3}}{x^4} = \frac{x^6}{x^4} = x^{6-4} = x^2 \).

Raising a negative number to an odd exponent results in a negative outcome, so \( (-3)^5 = -243 \).

Any non-zero number raised to the power of zero equals 1. This is a fundamental property in exponents, simplifying many expressions in mathematics.

By applying the Power of a Product rule, \( (x^3y^2)^2 = x^{3 \times 2}y^{2 \times 2} = x^6y^4 \).

The Product Law states that when you multiply two powers with the same base, you add the exponents, as in \( a^m \times a^n = a^{m+n} \).

Simplifying gives \( \frac{a^{2+3}}{a^4} = \frac{a^5}{a^4} = a^{5-4} = a^1 \).

The expression \( 5^{3/2} \) can be rewritten as \( \sqrt{5^3} \) or \( \sqrt{5}^3 \). Thus, \( 5^{3/2} = \sqrt{5}^3 \).

\( a^{1/2} \) represents the square root, so \( 4^{1/2} = \sqrt{4} = 2 \).

Using the Power Law, \( (3^2)^3 = 3^{2 \times 3} = 3^6 \). This demonstrates how to multiply exponents when raising a power to another power.

A negative exponent indicates the reciprocal of the base raised to the positive exponent, hence \( a^{-n} = \frac{1}{a^n} \).

\( 5^{-2} = \frac{1}{5^2} = \frac{1}{25} = 0.04 \). This illustrates how negative exponents simplify into fractions.

Using the Quotient Law, \( 9^{x+1} \div 9^{x-2} = 9^{(x+1)-(x-2)} = 9^{3} \).

The exponent \( m \) indicates how many times the base \( a \) is multiplied by itself. For example, \( a^3 \) means \( a \times a \times a \).

The square root of a number can be expressed as that number raised to the \( \frac{1}{2} \) power, so \( \sqrt{16} = 16^{1/2} = 4 \).

By applying the Product Law, \( 2^3 \times 2^{-5} = 2^{3-5} = 2^{-2} \). This shows how to combine powers with the same base.

Calculating yields \( \frac{2^3 \times 4^2}{4^3} = 2^3 \times 4^{2-3} = 2^3 \times 4^{-1} \).

Since \( m \) is even, \( (-2)^4 = 16 \). Even exponents of negative bases yield positive results.

Using the Power of a Product rule, \( (2 \times 3)^2 = (6)^2 = 36 \). This shows how to apply the exponent to the product of two bases.

According to the Quotient Law, when dividing, you subtract the exponents: \( a^m \div a^n = a^{m-n} \).