Advanced problem solving with the laws of indices | Maths

Starter quiz

Evaluate $16^\frac{1}{2}$ , giving the positive solution where necessary.

'4' ✓
Evaluate $9^\frac{3}{2}$ , giving the positive solution where necessary.

'27' ✓
Evaluate $25^\frac{1}{2}$ , giving the positive solution where necessary.

'5' ✓
What is the value of $b$ for $b^7 \div b^5 =9^2$ ?

'9' ✓
What is the value of $k$ for $0.2^5 \div 0.2^k = 0.2^7$ ?

'-2' ✓
What number is written as $2^3 \times 5 \times 7$ as a product of its prime factors?

'280' ✓

What is the value of $x$ for $(3^3)^4 × 3^2 = 3^x$ ?

'14' ✓
What is the value of $x$ for $\frac{2^{12} \times 2^4}{2^{10}} = 2^x$ ?

'6' ✓
What is the value of $x$ for $\frac{5^{14} \times 5^5}{5^{-2}} = 5^x$ ?

'21' ✓
What is the value of $x$ for $3^2 \times 3^6 = 9^x$ ?

'4' ✓
What is the value of $x$ for $2^3 \times 4^3 = 2^x$ ?

'9' ✓
What is the value of $x^{4x}$ for $2^x \times 2^{3x} = x^{4x}$ ?

'256' ✓

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Surds can be written in index notation.
The base could be a number, letter or combination of the two.
The laws are another way you can simplify an expression.
Plotting numbers against their squared values can help you estimate unknown amounts.

Using the laws of indices, when dividing by a number with a negative exponent pupils can incorrectly subtract the negative exponent.

When the bases of all the numbers are the same, forming an equation with the exponents can reduce errors.

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