EXAMPLES:
Question:
Write
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$\,(3x)^2\,$ in the form $\,kx^n\,$.
Solution:
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$(3x)^2 = 3^2x^2 = 9x^2\,$
or
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$(3x)^2 = (3x)(3x) = (3\cdot 3)(x\cdot x) = 9x^2$
Question:
Write
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$\,(2x)^3\,$ in the form $\,kx^n\,$.
Solution:
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$(2x)^3 = 2^3x^3 = 8x^3\,$
or
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$(2x)^3 = (2x)(2x)(2x) = (2\cdot 2\cdot 2)(x\cdot x\cdot x) = 8x^3$
Question:
Write
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$\,(-3x)^2\,$ in the form $\,kx^n\,$.
Solution:
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$(-3x)^2 = (-3)^2x^2 = 9x^2\,$
or
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$(-3x)^2 = (-3x)(-3x) = (-3\cdot -3)(x\cdot x) = 9x^2$
For mental math, the following thought process can be used:
- it's a negative number to an even power; so, the answer will be positive
- What's the size of the answer? $3^2 = 9$
- What's the variable part? $x^2$
- put it together to get $\,9x^2$
Question:
Write
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$\,(-2x)^3\,$ in the form $\,kx^n\,$.
Solution:
[beautiful math coming... please be patient]
$(-2x)^3 = (-2)^3x^3 = -8x^3\,$
or
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$(-2x)^3 = (-2x)(-2x)(-2x) = (-2\cdot -2\cdot -2)(x\cdot x\cdot x) = -8x^3$
For mental math, the following thought process can be used:
- it's a negative number to an odd power; so, the answer will be negative
- What's the size of the answer? $2^3 = 8$
- What's the variable part? $x^3$
- put it together to get $\,-8x^3$
Helpful facts to remember:
$2^5 = 32$
$3^4 = 81$
$3^5 = 243$
$4^3 = 64$
$5^3 = 125$