ACT 1 Alg: Use properties of exponents

$Q_{1}:$ Write an algebraic expression for the verbal expression " Ten less than one-fourth the cube of $p$"

$Q_{2}:$ An expression $5^{9}$ equal

$Q_{3}:$ Simplify $(-2ab^{2})(3a^{5}b^{3})=$

$Q_{4}:$ Simplify $( ( y^{2} )^{3} )^{4}$

$Q_{5}:$ Simplify $a^{n-2} . x . x^{n+1}$

$Q_{6}:$ Simplify $\frac{a^{7} b^{4} c^{2}}{a^{5} b^{2} c}$

$Q_{7}:$ Simplify $( \frac{8a^{-1}d^{3}c}{b^{2}d^{6}} )^{0}$

$Q_{8}:$ Simplify $( \frac{12s^{2}}{6t})^{-3}$

$Q_{9}:$ Simplify $\frac{ a^{-2} b^{3} c^{-3} }{ ab^{-2} }$

$Q_{10}:$ Simplify $(5 \times 10^{-12})(5 \times 10^{4})$

$Q_{11}:$ Write this number $ \frac{9 \times 10^{3}}{ 3 \times 10^{-4} } $ in decimal form

$Q_{12}:$ Write this number $248623$ in scientific notation.

$Q_{13}:$ Write this number $0.00000107000$ in scientific notation.

$Q_{14}:$ If $(-a^{2}b^{3})(2ab^{2})(-3b)= ka^{m} b^{n}$, what is the value of $m+n$?

$Q_{15}:$ If $(\frac{2a^{2}b}{3})^{2} (\frac{4ab}{3} )^{-3}=ka^{m}b^{n}$ , what is the value of $k $?

$Q_{16}:$ If $ \frac{x^{3}(-y)^{2}(z^{-2})}{x^{-2}y^{3}z} =\frac{x^{m}}{y^{n}z^{p}} $, what is the value of $m+n+p$?

$Q_{17}:$ If $2^{x}=5$, what is the value of $2^{x}+2^{2x}+2^{3x}$?

$Q_{18}:$ Which of the following is equivalent to the expression $(3^{x}+3^{x}+3^{x}). 3^{x}$?

$Q_{19}:$ If the expression $\frac{(6xy^{2})(2xy)^{2}}{8x^{2}y^{2}}$ is written in the form $ax^{m}y^{n}$, what is the value of $m+n$?

$Q_{20}:$ If $x$ is not equal to zero, what is the value of $\frac{(2x)^{3}(3x)}{(6x^{2})^{2}}$?

$Q_{21}:$ If $8200\times 300000$ is equal to $2.46\times 10^{n}$, what is the value of $n $?

$Q_{22}:$ If $\frac{240}{80000} \times \frac{6000}{9000000}$ is equal to $\frac{1}{5\times 10^{n}}$, what is the value of $n $?

$Q_{23}:$ If $12^{99}-12^{97}=12^{97} \times n$, what is the value of $n $?

$Q_{24}:$ Which of the following is equivalent to the expression $\frac{2^{(a+b)^{2}}}{2^{(a-b)^{2}}$?

$Q_{25}:$ If $8^{\frac{4}{3}}. 8^{\frac{8}{3}}=\frac{1}{2^{m}}$, what is the value of $m $?