Photo AI

10 (a) Simplify $$\left( \frac{1}{m} \right)^{y}$$ (b) Simplify $$\frac{8(x - 4)}{(x - 4)^{2}}$$ (c) Simplify $$(3n^{2}w^{3})^{y}$$ - Edexcel - GCSE Maths - Question 12 - 2020 - Paper 2

Question icon

Question 12

10-(a)-Simplify---$$\left(-\frac{1}{m}-\right)^{y}$$----(b)-Simplify---$$\frac{8(x---4)}{(x---4)^{2}}$$----(c)-Simplify---$$(3n^{2}w^{3})^{y}$$----Edexcel-GCSE Maths-Question 12-2020-Paper 2.png

10 (a) Simplify $$\left( \frac{1}{m} \right)^{y}$$ (b) Simplify $$\frac{8(x - 4)}{(x - 4)^{2}}$$ (c) Simplify $$(3n^{2}w^{3})^{y}$$

Worked Solution & Example Answer:10 (a) Simplify $$\left( \frac{1}{m} \right)^{y}$$ (b) Simplify $$\frac{8(x - 4)}{(x - 4)^{2}}$$ (c) Simplify $$(3n^{2}w^{3})^{y}$$ - Edexcel - GCSE Maths - Question 12 - 2020 - Paper 2

Step 1

Simplify $$\left( \frac{1}{m} \right)^{y}$$

96%

114 rated

Answer

Using the property of exponents that states (ab)c=ab⋅c\left( a^{b} \right)^{c} = a^{b \cdot c}, we can simplify this expression as follows:

(1m)y=1ymy=1my.\left( \frac{1}{m} \right)^{y} = \frac{1^{y}}{m^{y}} = \frac{1}{m^{y}}. Thus, the answer is ( \frac{1}{m^{y}} ).

Step 2

Simplify $$\frac{8(x - 4)}{(x - 4)^{2}}$$

99%

104 rated

Answer

To simplify the given fraction, we can cancel one factor of ( (x - 4) ) in the numerator and denominator:

8(x−4)(x−4)2=8(x−4).\frac{8(x - 4)}{(x - 4)^{2}} = \frac{8}{(x - 4)}. So, the simplified form is ( \frac{8}{x - 4} ).

Step 3

Simplify $$(3n^{2}w^{3})^{y}$$

96%

101 rated

Answer

Applying the property of exponents to each factor inside the parentheses, we get:

(3n2w3)y=3y(n2)y(w3)y=3yn2yw3y.(3n^{2}w^{3})^{y} = 3^{y}(n^{2})^{y}(w^{3})^{y} = 3^{y}n^{2y}w^{3y}. Hence, the simplified expression is ( 3^{y} n^{2y} w^{3y} ).

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;