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write in the form c (a^p) (b^q)
- Thread starter CB1101
- Start date
Is this the expression you are supposed to restate: \(\displaystyle \dfrac{a(a/b)}{3/a}.\)a(a/b)
3/a
my work:
a(a/b)
3/a
(a^2)(2/b)
3
Where did the 2 come from?
(3a^2)(2/b)
I have it mostly in the proper format except for the (b^q)
What exponent does b need to equal 2/b?
Let's simplify the fraction first
\(\displaystyle \dfrac{a(a/b)}{3/a} = a(a/b) * \dfrac{a}{3}.\) Invert and multiply: you learned that in 3rd or 4th grade. So
\(\displaystyle \dfrac{a(a/b)}{3/a} = \dfrac{a^2}{b} * \dfrac{a}{3} = \dfrac{1}{3} * \dfrac{a^3}{b}.\)
What is the meaning of a negative exponent?
I may have made a mistake in copying the numbers into the post.
A negative exponent tells you how many times to divide by the number, so...
(1/3) (a^3) (b^-1)
But the expression was actually \(\displaystyle \dfrac{a(2/b)}{3/a}\)
a(2/b)
3/a
a(2/b)
3a^-1 ........... turned the fraction in the denominator into a negative exponent
3a(2/b)
a^-1 ............ multied whole expression by 3
3a^2(2/b)
1 ................. divided a^-1 from denominator into a in the numerator
But I'm still left with 2/b. Not sure what negative exponent to use there. Let me know if I've made a mistake.
A negative exponent tells you how many times to divide by the number, so...
(1/3) (a^3) (b^-1)
But the expression was actually \(\displaystyle \dfrac{a(2/b)}{3/a}\)
a(2/b)
3/a
a(2/b)
3a^-1 ........... turned the fraction in the denominator into a negative exponent
3a(2/b)
a^-1 ............ multied whole expression by 3
3a^2(2/b)
1 ................. divided a^-1 from denominator into a in the numerator
But I'm still left with 2/b. Not sure what negative exponent to use there. Let me know if I've made a mistake.
\(\displaystyle \dfrac{a(2/b)}{3/a} = \)I may have made a mistake in copying the numbers into the post.
A negative exponent tells you how many times to divide by the number, so...
(1/3) (a^3) (b^-1) correct YES
But the expression was actually \(\displaystyle \dfrac{a(2/b)}{3/a}\)
a(2/b)
3/a
a(2/b)
3a^-1 ........... turned the fraction in the denominator into a negative exponent
3a(2/b)
a^-1 ............ multied whole expression by 3 This changes the value. You can't switch a factor from denominator to numerator.
3a^2(2/b)
1 ................. divided a^-1 from denominator into a in the numerator
But I'm still left with 2/b. Not sure what negative exponent to use there. Let me know if I've made a mistake.
\(\displaystyle \dfrac{2a}{b} * \dfrac{a}{3} = \dfrac{2a^2}{3b} = \dfrac{2}{3} * a^2 * \dfrac{1}{b}.\)
And \(\displaystyle \dfrac{1}{b}\) is what in exponential form.
\(\displaystyle \dfrac{a(2/b)}{3/a} = \)
\(\displaystyle \dfrac{2a}{b} * \dfrac{a}{3} = \dfrac{2a^2}{3b} = \dfrac{2}{3} * a^2 * \dfrac{1}{b}.\)
And \(\displaystyle \dfrac{1}{b}\) is what in exponential form.
b^-1
Thanks a ton