simplify:(6^-1 x3^-2)÷7^2
Answers
Answer:
Example 1: Simplifying ~\dfrac{10x^3}{2x^2-18x}
2x
2
−18x
10x
3
space, start fraction, 10, x, cubed, divided by, 2, x, squared, minus, 18, x, end fraction
Step 1: Factor the numerator and denominator
Here it is important to notice that while the numerator is a monomial, we can factor this as well.
\dfrac{10x^3}{2x^2-18x}=\dfrac{ 2\cdot 5\cdot x\cdot x^2}{ 2\cdot x\cdot (x-9)}
2x
2
−18x
10x
3
=
2⋅x⋅(x−9)
2⋅5⋅x⋅x
2
start fraction, 10, x, cubed, divided by, 2, x, squared, minus, 18, x, end fraction, equals, start fraction, 2, dot, 5, dot, x, dot, x, squared, divided by, 2, dot, x, dot, left parenthesis, x, minus, 9, right parenthesis, end fraction
Step 2: List restricted values
From the factored form, we see that {x\neq0}x
=0x, does not equal, 0 and {x\neq9}x
=9x, does not equal, 9.
Step 3: Cancel common factors
\begin{aligned}\dfrac{ \tealD 2\cdot 5\cdot \purpleC{x}\cdot x^2}{ \tealD 2\cdot \purpleC{x}\cdot (x-9)}&=\dfrac{ \tealD{\cancel{ 2}}\cdot 5\cdot \purpleC{\cancel{x}}\cdot x^2}{ \tealD{\cancel{ 2}}\cdot \purpleC{\cancel{x}}\cdot (x-9)}\\ \\ &=\dfrac{5x^2}{x-9} \end{aligned}
2⋅x⋅(x−9)
2⋅5⋅x⋅x
2
=
2
⋅
x
⋅(x−9)
2
⋅5⋅
x
⋅x
2
=
x−9
5x
2
Step 4: Final answer
We write the simplified form as follows:
\dfrac{5x^2}{x-9}
x−9
5x
2
start fraction, 5, x, squared, divided by, x, minus, 9, end fraction for x\neq 0x
=0x, does not equal, 0
[Why do we require x≠0?]
Step-by-step explanation:
Hope it is helpful buddy.
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