Question

Simplify the product using the rules for exponents: 19(3) × 19(4) exponents are in parentheses... Choices are as follows: 19 × 7 B. 1912 C. 19−1 D. 197

Answer 1

By the rules of exponents;
\[x^{3}\times x^{4}=(xxx)(xxxx)=xxxxxxx=x ^{7}\]
So,
\[19^{3}\times 19^{4}=\left( 19\times 19\times19 \right)\times \left( 19\times19\times19\times19 \right)=19^{7}\]

Answer 2

But remember, that they have to have the same base in order to just add the exponents together.

Answer 3

ok so add all exponents or multiply or whatever but the base is always the same?

Answer 4

The base is the number the exponent is stuck with so the base of;
\[x^{2}\]
is the x.
Now if you have;
\[x^{2}\times x^{3}\]
Both have the base of x, so you just add the exponents;
\[x^{2}\times x^{3}=x^{2+3}=x^{5}\]
But if they have different bases, say;
\[x^{2}\times y^{3}\]
They have different bases, being x and y. So you can't combine exponents by simply adding them.