The laws of indices - fractional exponents | Maths | Quizalize & Oak National Academy

Starter quiz

What is the value of $x$ for $(m^x)^8 = m^{32}$

'4' ✓
What is the value of $x$ for $(m^{-2})^5 = m^x$

'-10' ✓
What is the value of $x$ for $(m^8)^x = m^{80}$

'10' ✓
What is the value of $x$ for $\frac{1}{16} = 2^x$

'-4' ✓
What is the value of $x$ for $\frac{1}{64} = x^{-6}$

'2' ✓
What is the value of $a$ for $7^9 \times 7^a = 7^6$ ?

'-3' ✓

Exit quiz

Evaluate $36^{\frac{1}{2}}$ , giving the positive solution where necessary.

'6' ✓
Evaluate $1000^{\frac{1}{3}}$ , giving the positive solution where necessary.

'10' ✓
Evaluate $27^{\frac{2}{3}}$ , giving the positive solution where necessary.

'9' ✓
Evaluate $1000^{\frac{2}{3}}$ , giving the positive solution where necessary.

'100' ✓
Evaluate $16^{\frac{3}{4}}$ , giving the positive solution where necessary.

'8' ✓
Evaluate $16^{\frac{3}{2}}$ , giving the positive solution where necessary.

'64' ✓

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

All of the index laws can be applied with fractional exponents.
Using a calculator can help you to form an idea about how to evaluate a power containing a fractional exponent.
You can reason that a power with a fractional exponent is equivalent to finding the square root of the base.
√a = a^(1/2)

Common misconception

Pupils multiply the base by the fractional exponent. e.g 25^(1/2) = 12.5

The use of a calculator allows pupils to see the index of a fraction is not to be multiplied by the base. Embedding the laws of indices where two bases are the same and each number has an index of 1/2 helps recognize the 1/2 index as a square root.

Keywords

Reciprocal - A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.