Question 630183
Important: Exponents only apply to what is literally in front of them!<br>
In {{{-5x^2}}} it is the "x" that is in front of the exponent. So the exponent applies only to the x. So {{{-5x^2}}} is short for {{{-5*x*x}}}.<br>
In {{{(-5x)^2}}} it is the right parenthesis that is in front of the exponent. This means that the exponent applies to the whole expression inside the parentheses. So {{{(-5x)^2}}} is short for {{{(-5x)*(-5x)}}} (which simplifies to {{{25x^2}}}).<br>
One of the rules/properties of exponents is:
{{{a^n*b^n = (a*b)^n}}}
The expression
{{{2^7*5^7}}}
matches the pattern of the left side of the rule above. So according to the rule it must be equal to the right side of the rule:
{{{(2*5)^7}}}
which simplifies to
{{{10^7}}}<br>
As usual, if you have trouble using the rules for exponents, work without them! In other words, rewrite your expressions without exponents and simplify without them.
{{{2^7*5^7}}}
becomes
2*2*2*2*2*2*2*5*5*5*5*5*5*5
This is all multiplication so we can use the Commutative Property of Multiplication to change the order as we please and we can use the Associative Property of Multiplication to rearrange the grouping as we please. So we can change the above to:
(2*5)*(2*5)*(2*5)*(2*5)*(2*5)*(2*5)*(2*5)
which simplifies to:
(10)*(10)*(10)*(10)*(10)*(10)*(10)
which can be rewritten as
{{{10^7}}}