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CanadaON
Grade 12

Simplify expressions using multiple exponent laws with integer and variable bases

Lesson

We've learnt lots of exponent laws now: the multiplication law, the division law, the power of a power law and the zero exponent law.

Now we are going to look at questions that we solve by using a combination of these rules. It's important to remember the order of operations when solving these questions as this is the order we apply.

Examples

Question 1

Simplify: $p^7\div p^3\times p^5$p7÷​p3×p5.

Think: Following the order of operations, we'll use the division law and the multiplication law since they all have like bases.

Do:

$p^7\div p^3\times p^5$p7÷​p3×p5 $=$= $p^{7-3+5}$p73+5
  $=$= $p^9$p9

 

Question 2

Simplify $\frac{\left(x^2\right)^6}{\left(x^2\right)^2}$(x2)6(x2)2

Question 3

Simplify $\left(u^9\times u^5\div u^{19}\right)^2$(u9×u5÷​u19)2, expressing your answer in positive exponential form.

 

Outcomes

12CT.A.2.1

Simplify algebraic expressions containing integer and rational exponents using the laws of exponents (e.g., x^3/x^(1/2), sqrt(x^6 y^12))

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