Easy question on converting powered terms to base

[Andrew Rubin]

Hi

I have really easy question that I can't find the answer to neither in my mathematics textbook or other sources online. I'm working on exponential functions and logarithms, before starting on integration.

The chapter starts of with this equation:

[MATH]\left(10^{-2}\right)^x=10^3\cdot 10^{\frac{1}{2}}[/MATH]
is equivalent to,

[MATH]10^{-2x}=10^{\frac{7}{2}}[/MATH]
After converting [MATH]10^3\cdot \:10^{\frac{1}{2}}[/MATH] to base 10.

It seems so easy, but I cannot calculate how [MATH]10^3\cdot 10^{\frac{1}{2}}[/MATH] becomes [MATH]10^{\frac{7}{2}}[/MATH].

Can someone on this forum help me out?

 

[Dr.Peterson]

I'm not sure what you mean by "converting to base 10". But [MATH]10^3\cdot10^{\frac{1}{2}} = 10^{3+\frac{1}{2}} = 10^{\frac{7}{2}}[/MATH].

 

[JeffM]

[MATH]10^3 * 10^{1/2} = 10^{\{3 + (1/2)\}} = 10^{\{(6/2)+(1/2)\}} = 10^{7/2}.[/MATH]

 

[Deleted member 4993]

Hi

I have really easy question that I can't find the answer to neither in my mathematics textbook or other sources online. I'm working on exponential functions and logarithms, before starting on integration.

The chapter starts of with this equation:

[MATH]\left(10^{-2}\right)^x=10^3\cdot 10^{\frac{1}{2}}[/MATH]
is equivalent to,

[MATH]10^{-2x}=10^{\frac{7}{2}}[/MATH]
After converting [MATH]10^3\cdot \:10^{\frac{1}{2}}[/MATH] to base 10.

It seems so easy, but I cannot calculate how [MATH]10^3\cdot 10^{\frac{1}{2}}[/MATH] becomes [MATH]10^{\frac{7}{2}}[/MATH].

Can someone on this forum help me out?

The calculations above was done by using Laws of Exponents. Are you familiar with Laws of Exponents ( https://www.mathsisfun.com/algebra/exponent-laws.html )?

 

[Andrew Rubin]

Thank you for all your good replies! Both the calculations showing steps and the list for Laws of Exponents was very helpful.