Warm up Simplify the following expressions a 4

Warm up • Simplify the following expressions: • a) (4 x 3)(3 x 4) • b) (27 x 4) ÷ (3 x 2) • c) (5 x 4 y 3)2

We are Learning to…… Use Fractional Exponents

Exponent notation We use exponent notation to show repeated multiplication by the same number. For example: we can use exponent notation to write 2 × 2 × 2 as 25 Exponent or power base This number is read as ‘two to the power of five’. 25 = 2 × 2 × 2 = 32

Exponent laws Here is a summary of the exponent laws you have met so far: xm × xn = x(m + n) xm ÷ xn = x(m – n) (xm)n = xmn x 1 = x x 0 = 1 (for x = 0) 4 of 70 © Boardworks Ltd 2005

Exponent laws for negative exponents Here is a summary of the exponent laws for negative exponents. x– 1 = 1 x x–n 5 of 70 = 1 n x The reciprocal of x is The reciprocal of xn 1 x 1 is n x © Boardworks Ltd 2005

Fractional exponents 1 2 Exponents can also be fractional. Suppose we have 9. 1 2 9 × 9 = 9 In general, 6 of 70 1 2 = 91 = 9 Because 3 × 3 = 9 1 x 2 = x In general, But, + 9 × 9 = 9 But, Similarly, 1 2 1 3 1 3 8 × 8 = 8 3 1 1 1 3+ 3+ 3 3 3 = 81 = 8 8 × 8 = 8 1 Because 2× 2× 2=8 3 x 3 = x © Boardworks Ltd 2005

Fractional exponents 3 2 What is the value of 25 ? 3 2 We can think of 25 as 25 1 2 × 3 . Using the rule that (xa)b = xab we can write 25 1 2 × 3 = ( 25)3 = (5)3 = 125 In general, m n n x = ( x)m 7 of 70 © Boardworks Ltd 2005

Evaluate the following 49 12 = √ 49 = 7 1) 49 12 2) 1000 23 = (3√ 1000)2 = 100 3) 1 8 - 3 1 83 4) 2 64 - 3 64 - 5) 4 8 of 70 2 3 5 2 1 1 1 = 3 = √ 8 83 2 2 3 1 1 = 2 = 3 2 3 ( √ 64) 64 4 16 4 52 = (√ 4)5 = 25 = 32 © Boardworks Ltd 2005

Exponent laws for fractional exponents Here is a summary of the exponent laws for fractional exponents. x = x 1 2 n x = x 1 n m n x = 9 of 70 n xm n or ( x)m © Boardworks Ltd 2005

• To succeed at this lesson today you need to know and be able to use… • 1. The five basic exponent laws • 2. Negative exponents • 3. Fractional exponents Nelson Page 229 #s 1 – 3, 5 ace, 6 adf & 7 Page 236 #s 4 – 6