44457.Simplify : a4b2 x a2b2
a4b4
a6b4
a4b2
a2b4
Explanation:
a4b2 x a2b2=a4+2b2+2 [ Using Rule am x an = am + n ]
= a6b4
a4b2 x a2b2=a4+2b2+2 [ Using Rule am x an = am + n ]
= a6b4
44458.Simplify : 5(8x4 $\div$ 2x6)
$\dfrac{8}{x^{2}}$
$\dfrac{2}{x^{2}}$
$\dfrac{20}{x^{2}}$
$\dfrac{20}{x^{4}}$
Explanation:
5(8x4 $\div$ 2x6) [since a$\div$b=$\dfrac{a}{b}$ , split the equation to make it easier to solve]
=5(8 $\div$ 2)(x4 $\div$ x6) [Get the quotient of 8 and 2.]
=5(4)(x4-6) [Using Rule $a^{m}\div a^{n}= a^{m - n}$]
=20(x-2) [Get the product of 5 and 4]
=$\dfrac{20}{x^{2}}$ [Using Rule $a^{-m}=\dfrac{1}{a^{m}}$]
5(8x4 $\div$ 2x6) [since a$\div$b=$\dfrac{a}{b}$ , split the equation to make it easier to solve]
=5(8 $\div$ 2)(x4 $\div$ x6) [Get the quotient of 8 and 2.]
=5(4)(x4-6) [Using Rule $a^{m}\div a^{n}= a^{m - n}$]
=20(x-2) [Get the product of 5 and 4]
=$\dfrac{20}{x^{2}}$ [Using Rule $a^{-m}=\dfrac{1}{a^{m}}$]
44459.Simplify : $\left( \dfrac{5a}{b^{2}}\right)^{2}$
$\dfrac{5a^{2}}{b^{4}}$
$\dfrac{25a^{2}}{b^{2}}$
$\dfrac{25a^{2}}{b^{4}}$
$\dfrac{5a^{2}}{b^{2}}$
Explanation:
$\left( \dfrac{5a}{b^{2}}\right)^{2} =\dfrac{ 5^{2}a^{2}}{b^{2 \times 2}}$ [Using Rule $(a^{m})^{n} = a^{mn}$]
=$\dfrac{25a^{2}}{b^{4}}$ [Evaluate 52]
$\left( \dfrac{5a}{b^{2}}\right)^{2} =\dfrac{ 5^{2}a^{2}}{b^{2 \times 2}}$ [Using Rule $(a^{m})^{n} = a^{mn}$]
=$\dfrac{25a^{2}}{b^{4}}$ [Evaluate 52]
44460.Simplify : 5*82/3
5
8
40
20
Explanation:
5*82/3
= 5*$(\sqrt[3]{8})^{2}$ [using Rule am/n=$\sqrt[n]{a^{m}}=(\sqrt[n]{a})^{m}$]
=5*22 [Get the value of $\sqrt[3]{8}$]
=5*4 [Get the value of 22]
=20 [Get the product of 5 and 4]
5*82/3
= 5*$(\sqrt[3]{8})^{2}$ [using Rule am/n=$\sqrt[n]{a^{m}}=(\sqrt[n]{a})^{m}$]
=5*22 [Get the value of $\sqrt[3]{8}$]
=5*4 [Get the value of 22]
=20 [Get the product of 5 and 4]