+72 a. Show, by exapnding, that 310=95
b. Show, using index laws, that 310=95
Don't they just mean the same thing?
Help me please :)
+26367 a. Show, by expanding, that 310=95
b. Show, using index laws, that 310=95
Don't they just mean the same thing?
I assume
a.
\(\begin{array}{rcll} 3^{10} &=& 9^5 \\ 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3 &=& 9\cdot 9\cdot 9\cdot 9\cdot 9 \\ 59049 &=& 59049 \end{array}\)
b.
\(\begin{array}{rcll} 3^{10} &=& 9^5 \\ 3^{2\cdot 5} &=& 9^5 \\ (3^2)^5 &=& 9^5 \\ 9^5 &=& 9^5 \\ \end{array}\)
+72 Would you mind explaining 'b' in a little bit more detail? as in how you got that answer?
+26367 b. Show, using index laws, that 310=95
\(\begin{array}{lrcll} & 3^{{\color{red}10}} &=& 9^5 \quad & | \qquad {\color{red}10} = 2\cdot 5\\ & 3^{2\cdot 5} &=& 9^5 \\\\ \hline \\ \text{formula: } & \boxed{~ \begin{array}{rcll} (a^b)^c = a^{b\cdot c} = a^{c\cdot b} = (a^c)^b \end{array} ~} \\ \\ \hline \\ & (3^2)^5 &=& 9^5 \quad & | \qquad 3^{2\cdot 5} = (3^2)^5\\ & ({\color{green}3^2})^5 &=& 9^5 \quad & | \qquad {\color{green}3^2} = 3\cdot 3 = 9\\ & 9^5 &=& 9^5 \\ \end{array}\)
see: https://www.mathsisfun.com/algebra/exponent-laws.html
