Question

How do you write nine to the \[{y^{th}}\] power in exponential form?

Answer 1

Hint: Exponential notation is an alternative method of expressing numbers. Exponential numbers take the form \[{a^n}\], where a is multiplied by itself n times. In exponential notation, a is termed the base while n is termed the power or exponent or index. As given here, nine is multiplied by itself y times, hence based on this we need to write in exponential form.

Complete step by step answer:
Given,
We need to write nine to the \[{y^{th}}\]power in exponential form: As nine to the \[{y^{th}}\] power implies that 9 is multiplied by itself y times.
Here, 9 is the base and y is the exponent, hence the exponential form is \[{9^y}\].

Additional information:
Scientific Notation Rules: To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.
If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive.
Example: \[6000 = 6 \times {10^3}\] is in scientific notation.
If the given number is smaller than 1, then the decimal point has to move to the right, so the power of 10 will be negative.
Example: \[0.006 = 6 \times 0.001 = 6 \times {10^{ - 3}}\] is in scientific notation.

Note: When the scientific notation of any large numbers is expressed, then we use positive exponents for base 10 i.e., for example:
\[200000 = 2 \times {10^5}\], where 5 is the positive exponent.
When the scientific notation of any small numbers is expressed, then we use negative exponents for base 10 i.e., for example:
\[0.00002 = 2 \times {10^{ - 5}}\], where -5 is the negative exponent.
Hence, in this way we need to write the given number in exponential form.