Question

Simplify: ${( - 3)^2} \times {( - 5)^2}$

Answer 1

Hint: In mathematical expression, generally the power is used to express the long expression in the short form that is used generally to represent the repeated multiplication of the same factor. Here we will use the power and exponent rule to simplify the given expression.

Complete step-by-step answer:
Take the given expression: ${( - 3)^2} \times {( - 5)^2}$
Apply the power of product rule - When powers are equal, then the bases are combined which can be expressed as – ${a^2} \times {b^2} = {(a \times b)^2}$
So, the above expression can be re-written as –
$ = {\left( {( - 3) \times ( - 5)} \right)^2}$
When you multiply two negative terms, the resultant value is positive because minus with minus gives plus.
$ = {\left( {15} \right)^2} = 225 $
Hence, the required simplified form of the given expression ${( - 3)^2} \times {( - 5)^2}$ can be as ${\left( {15} \right)^2}$ which is equal to 225.
So, the correct answer is “225”.

Note: Remember the seven basic rules of the exponent or the laws of exponents to solve these types of examples. Make sure to go through the below mentioned rules which defines how to solve different types of exponents problems and how to add, subtract, multiply and divide the exponents.
i.Product of powers rule
ii.Quotient of powers rule
iii.Power of a power rule
iv.Power of a product rule
v.Power of a quotient rule
vi.Zero power rule
vii.Negative exponent rule