Which expression is equivalent to (x^-4y/x^-9y^5)^-2 ? Assume x ≠ 0, y ≠ 0
A y^8/x^10
B x^5/y^7
C x^5/y^4
D x/y^7

Which expression is equivalent to 28p^9q^-5/12p^-6q^7 Assume p ≠ 0,q ≠ 0
A 2/p^15q^12
B 7p15/3q12
C 2q^12/p^15
D 7p^15q^12/3

Which expression is equivalent to (5ab)^3/30a^-6b^-7 ? Assume a ≠ 0, b ≠ 0
A a^7b^10/6
B 125a^18b^21/30
C 25a^3b^4/6
D 25a^9b^10/6

[tex](\dfrac{x^{-4}y}{x^{-9}y^5})^{-2}\\\\\\=(x^{-4+9}y^{1-5})^{-2}\\\\=(x^5y^{-4})^{-2}\\\\=x^{5\times (-2)}y^{-4\times (-2)}\\\\=x^{-10}y^8\\\\=\dfrac{y^8}{x^10}[/tex]

( since, we know that:

[tex]\dfrac{x^m}{x^n}=x^{m-n}[/tex]

Also,

[tex](x^m)^n=x^{m\times n}[/tex] )

Hence, option: A is correct.

Ques 2)

[tex]\dfrac{28p^9q^{-5}}{12p^{-6}q^7}\\\\\\=\dfrac{28}{12}\times (p^{9+6}q^{-5-7})\\\\=\dfrac{7}{3}\times (p^{15}q^{-12})\\\\=\dfrac{7p^{15}}{3q^{12}}[/tex]

Hence, option: B is correct.

Ques 3)

[tex]=\dfrac{(5ab)^3}{30a^{-6}b^{-7}}\\\\=\dfrac{125a^3b^3}{30a^{-6}b^{-7}}\\\\=\dfrac{125}{30}\times (a^{3+6}b^{3+7})\\\\=\dfrac{25}{6}\times (a^9b^{10})\\\\=\dfrac{25a^9b^{10}}{6}[/tex]

Hence, option: D is true.

ap8997154 ap8997154 · Answer 2 · 2022-02-08T08:05:54+01:00

To solve the problem we must know about the exponent properties.

What are the basic exponent properties?

A few basic properties of the exponents are,

[tex]{a^m} \cdot {a^n} = a^{(m+n)}[/tex]

[tex]\dfrac{a^m}{a^n} = a^{(m-n)}[/tex]

[tex]\sqrt[m]{a^n} = a^{\frac{n}{m}}[/tex]

[tex](a^m)^n = a^{m\times n}[/tex]

[tex](m\times n)^a = m^a\times n^a[/tex]

Which expression is equivalent to [tex](\dfrac{x^{-4}y}{x^{-9}y^5})[/tex] ?

[tex](\dfrac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex]

Using the property [tex]\dfrac{a^m}{a^n} = a^{(m-n)}[/tex],

[tex]=(x^{-4+9}\cdot y^{1-5})^{-2}\\\\=(x^5\cdot y^{-4})^{-2}\\\\[/tex]

Using the property [tex](a^m)^n = a^{m\times n}[/tex],

[tex]= x^{(5\times 2)}\cdot y^{(-4\times 2)}\\\\= x^{10}\cdot y^{-8}\\\\= \dfrac{x^{10}}{y^8}[/tex]

Thus, the solution of the expression is [tex]\dfrac{x^{10}}{y^8}[/tex].

Which expression is equal to Which expression is equivalent to [tex]\dfrac{28p^9q^{-5}}{12p^{-6}q^7}[/tex] ?

[tex]\dfrac{28p^9q^{-5}}{12p^{-6}q^7}[/tex]

Using the property [tex]\dfrac{a^m}{a^n} = a^{(m-n)}[/tex],

[tex]=\dfrac{28p^9q^{-5}}{12p^{-6}q^7}\\\\=\dfrac{7p^{(9+6)}\cdot q^{-5-7}}{3}\\\\=\dfrac{7p^{(15)}\cdot q^{-12}}{3}\\\\=\dfrac{7p^{(15)}} {3q^{12}}[/tex]

Thus, the solution to the expression is [tex]\dfrac{7p^{(15)}} {3q^{12}}[/tex].

Which expression is equivalent to [tex]\dfrac{(5ab)^3}{30a^{-6}b^{-7}}[/tex] ?

[tex]\dfrac{(5ab)^3}{30a^{-6}b^{-7}}[/tex]

Using the property [tex](a^m)^n = a^{m\times n}[/tex],

[tex]=\dfrac{5^3a^3b^3}{30a^{-6}b^{-7}}[/tex]

[tex]=\dfrac{125\cdot a^{(3+6)}\cdot b^{(3+7)}}{30}\\\\=\dfrac{25\cdot a^{9}\cdot b^{10}}{6}[/tex]

Thus, the solution of the expression is [tex]\dfrac{25a^{(3+6)}b^{(3+7)}}{6}[/tex].

Learn more about Exponents:

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